This paper contains also results of experiments with decision tables from UCI Machine Learning Repository. The consideration of irredundant rules only does not change the results of optimization. We can also change the order of optimization. We can describe all irredundant β-decision rules with minimum length, and after that among these rules describe all rules with maximum coverage. This algorithm finishes the partitioning of a subtable when its uncertainty is at most β.The graph Δβ(T) allows us to describe the whole set of so-called irredundant β-decision rules. Our algorithm constructs a directed acyclic graph Δβ(T) which nodes are subtables of the decision table T given by systems of equations of the kind “attribute = value”. localize rows in subtables of T with uncertainty at most β. For a nonnegative real number β, we consider β-decision rules that. We introduce an uncertainty measure R(T) which is the number of unordered pairs of rows with different decisions in the decision table T.

This paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to the length and coverage. Extensive experimental results on 11 real world data sets and a case study on a Protein-Protein Interaction (PPI) data set demonstrate the effectiveness of our proposed method. Multiple consensuses are finally obtained by applying consensus clustering algorithms to each cluster of the partition. A dynamic programming algorithm is proposed to obtain a flat partition from the hierarchical tree using the modularity measure. Instead of generating a single consensus, MCC organizes the different input clusterings into a hierarchical tree structure and allows for interactive exploration of multiple clustering solutions. In this paper, we develop a new framework, called Multiple Consensus Clustering (MCC), to explore multiple clustering views of a given dataset from a set of input clusterings. There is a significant drawback in generating a single consensus clustering since different input clusterings could differ. Given a set of input clusterings of a given dataset, consensus clustering aims to find a single final clustering which is a better fit in some sense than the existing clusterings.

No disk may be placed on top of a smaller disk.Consensus clustering has emerged as an important extension of the classical clustering problem.

a disk can only be moved if it is the uppermost disk on a stack.

Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e.

The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules: The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The Tower of Hanoi (also called the Tower of Brahma or Lucas’ Tower, and sometimes pluralized) is a mathematical game or puzzle.

Programming hanoi towers